Finite Group Databasebeta

← #11791410

Subgroups — #11791410

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6C2×#63568C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#71818—31nomaximal
9#70358—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#947C411yescharacteristic, complemented
15C3×#944C411yescharacteristic, complemented
16C3×#940C411yescharacteristic, complemented
17C3×#939—21no—
18C3×#939—21no—
19C3×#936C411yescharacteristic, complemented
20C3×C4×#67—21no—
21C3×C4×#67—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×Dic3⋊Dic3—21no—
26#63664—22no—
27C3×#837—22no—
28#63579—21no—
29#63569—22no—
30#63568—22no—
31#63554—21no—
32Dic3×C3⋊C8—21no—
33C3×#532—31no—
34#5832D311yescharacteristic
35C2×C3×#104—31no—
36C2×#837—31no—
37C2×#837—31no—
38C2×#837—31no—
39C2×#837—31no—
40C2×#837—61no—
41C2×#837D311yescharacteristic, complemented
42C2×#825—31no—
43Dic3×M16—31no—
44C4×C4⋊Dic3—31no—
45C4×Dic3⋊C4—31no—
46C2×#805—31no—
47C4×#208—31no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8C2×C411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4C2×C411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D411yescharacteristic
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2×C411yescharacteristic
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73#3748—21no—
74#3748D412yescomplemented
75C2×C3⋊(C3⋊C8)—21no—
76C3×#217—21no—
77C3×#217—21no—
78C3×(C2×D3)⋊C4—21no—
79C3×(C2×D3)⋊C4—21no—
80C3×Dic3⋊C4—21no—
81C3×Dic3⋊C4—21no—
82C3×C4×Dic3—21no—
83C3×C4×Dic3—21no—
84C3×C4×Dic3C2×C411yescharacteristic
85C3×C4×Dic3C2×C411yescharacteristic
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3D411yescharacteristic
88C3×#208—21no—
89C3×#208D412yescomplemented
90C2×C3×C3⋊C8—21no—
91Dic3⋊Dic3—24no—
92#1980—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C2×D311yescharacteristic
97C2×#235C2×D311yescharacteristic
98C2×C3×M16—31no—
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×#124—31no—
102C3×#124—31no—
103C3×#121—61no—
104C3×#121—61no—
105C3×C4×D4—61no—
106C3×C4×D4—61no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109#947Dic311yescharacteristic, complemented
110#944Dic311yescharacteristic, complemented
111#940Dic311yescharacteristic, complemented
112#939—21no—
113#939—21no—
114#936Dic311yescharacteristic, complemented
115C4×#67—21no—
116C4×#67—21no—
117C2×C4⋊Dic3—61no—
118C2×Dic3⋊C4—61no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—61no—
122C2×C4×Dic3C2×D311yescharacteristic
123C2×C4×Dic3C2×D311yescharacteristic
124C2×#208—31no—
125C2×#208—31no—
126C2×#208—61no—
127C2×#208C2×D311yescharacteristic
128C3×#104—62no—
129#837—22no—
130#837—62no—
131#837—62no—
132#837—62no—
133#837—64no—
134#837—62no—
135C3⋊#95—61no—
136C3⋊#95—61no—
137#825—62no—
138#815—61no—
139C8×Dic3—61no—
140#805—62no—
141#803—61no—
142C4×C3⋊C8—61no—
143C23×C32—21no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—21no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—41no—
151C32×D4—41no—
152C2×C32×C4—21no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4#4111yescharacteristic
160C2×C32×C4#4111yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3—41no—
164C3×#67—42no—
165C3×#67—41no—
166C3×#67—41no—
167C3×#67—42no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3C22⋊C411yescharacteristic
175C2×C3×Dic3C22⋊C411yescharacteristic
176C2×C3×Dic3C22⋊C411yescharacteristic
177C2×C3×Dic3C22⋊C411yescharacteristic
178C3×D12—21no—
179C3×D12—21no—
180C3×C4×D3—41no—
181C3×C4×D3—41no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—22no—
186#532—31no—
187C2×#104—31no—
188C2×#104—91no—
189C2×#104—91no—
190C2×#104—91no—
191C4×M16—91no—
192C4×C4⋊C4—91no—
193C3×#41—22no—
194C3×#41—22no—
195C3×#41—21no—
196C3×#41—21no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—41no—
204C3×#41—41no—
205C3×#41—61no—
206C3×#41—61no—
207C3×#41—61no—
208C3×#41—61no—
209C2×C3×Q8—21no—
210C2×C3×Q8—31no—
211C2×C3×Q8C4×D311yescharacteristic
212C2×C3×Q8C2×Dic311yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—31no—
217C2×C3×D4—41no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C2×C3×D4C4×D311yescharacteristic
222C2×C3×D4C2×Dic311yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—41no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—21no—
235C2×#67—21no—
236C22×Dic3—21no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—121no—
240C22×Dic3#6711yescharacteristic
241C22×Dic3#6711yescharacteristic
242#235—21no—
243#235—21no—
244#235—21no—
245#235—21no—
246C2×D12C2×Dic311yescharacteristic
247C2×C4×D3—21no—
248C2×Dic6C2×Dic311yescharacteristic
249C3×M16—32no—
250C3×M16—61no—
251C2×C3×C8—61no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C22⋊C4—61no—
255C3×C22⋊C4—61no—
256C3×C22⋊C4—61no—
257C3×C22⋊C4—61no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—61no—
263C3×C42—61no—
264#217—21no—
265#217—21no—
266(C2×D3)⋊C4—21no—
267(C2×D3)⋊C4—21no—
268C4⋊Dic3—64no—
269Dic3⋊C4—21no—
270Dic3⋊C4—21no—
271Dic3⋊C4—64no—
272C4×Dic3—21no—
273C4×Dic3—21no—
274C4×Dic3—62no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—121no—
280C4×Dic3C2×Dic311yescharacteristic
281C4×Dic3C2×Dic311yescharacteristic
282C4×Dic3#6711yescharacteristic
283C4×Dic3#6711yescharacteristic
284#208—21no—
285#208—32no—
286#208—32no—
287#208—62no—
288#208—61no—
289#208—61no—
290#208—121no—
291#208#6712yescomplemented
292C2×C3⋊C8—21no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—61no—
295C2×C3⋊C8—121no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32C2×C22⋊C411yescharacteristic
302C22×C32#12411yescharacteristic
303C22×C32#12711yescharacteristic
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—41no—
307C32×C4—41no—
308C32×C4C4×D411yescharacteristic
309C32×C4C4×D411yescharacteristic
310C32×C4#12111yescharacteristic
311C32×C4#12111yescharacteristic
312C3⋊Dic3—42no—
313C3×Dic3—21no—
314C3×Dic3—21no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3#10412yescomplemented
319C2×#41—31no—
320C2×#41D3211yescharacteristic
321C2×M16—31no—
322C2×M16—91no—
323C4⋊Q8—31no—
324#127—31no—
325#124—31no—
326#124—31no—
327#121—61no—
328#121—61no—
329C4×D4—61no—
330C4×D4—61no—
331C2×C4⋊C4—181no—
332C2×C42—31no—
333C2×C42—31no—
334C2×C42—91no—
335#104—62no—
336#104—182no—
337#104—182no—
338#104—182no—
339#97—181no—
340C4×C8—181no—
341#95—181no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—41no—
346C23×C3—61no—
347C23×C3D3×D411yescharacteristic
348C23×C3C2×#6711yescharacteristic
349C22×D3—21no—
350C3×Q8—22no—
351C3×Q8—21no—
352C3×Q8—21no—
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—41no—
356C3×Q8—61no—
357C3×Q8—61no—
358C3×D4—22no—
359C3×D4—21no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—41no—
364C3×D4—42no—
365C3×D4—42no—
366C3×D4—41no—
367C3×D4—41no—
368C3×D4—41no—
369C3×D4—41no—
370C3×D4—61no—
371C3×D4—61no—
372C3×D4—122no—
373C3×D4—122no—
374C3×D4—121no—
375C3×D4—121no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—121no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4C2×C4×D311yescharacteristic
404C2×C3×C4#23511yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4#23711yescharacteristic
410C2×C3×C4#23711yescharacteristic
411C2×C3×C4#23711yescharacteristic
412C2×C3×C4C22×Dic311yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415#67—42no—
416#67—41no—
417#67—41no—
418#67—42no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—21no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—122no—
432C2×Dic3—121no—
433C2×Dic3—121no—
434C2×Dic3#21711yescharacteristic
435C2×Dic3#21711yescharacteristic
436C2×Dic3#21711yescharacteristic
437C2×Dic3#21711yescharacteristic
438D12—21no—
439D12—21no—
440C4×D3—41no—
441C4×D3—41no—
442Dic6—21no—
443Dic6—21no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—122no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—81no—
452C2×C32#39011yescharacteristic
453C2×C32C2×#10411yescharacteristic
454C2×C32#42111yescharacteristic
455C3×D3—81no—
456#41—21no—
457#41—21no—
458#41—21no—
459#41—21no—
460#41—61no—
461#41—61no—
462#41—61no—
463#41—61no—
464C2×Q8—31no—
465C2×Q8D3×Dic311yescharacteristic
466C2×D4—21no—
467C2×D4—31no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4D3×Dic311yescharacteristic
472C22×C4—21no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—181no—
478C22×C4C2×D3211yescharacteristic
479M16—32no—
480M16—61no—
481M16—92no—
482M16—181no—
483C2×C8—61no—
484C2×C8—181no—
485C4⋊C4—61no—
486C4⋊C4—61no—
487C4⋊C4—184no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—61no—
491C22⋊C4—61no—
492C42—31no—
493C42—31no—
494C42—31no—
495C42—31no—
496C42—61no—
497C42—61no—
498C42—181no—
499C42—181no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—42no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3—121no—
521C22×C3D3×C22⋊C411yescharacteristic
522C22×C3#88511yescharacteristic
523C22×C3#93611yescharacteristic
524C22×C3#94011yescharacteristic
525C22×C3#94011yescharacteristic
526C22×C3C2×#21711yescharacteristic
527C2×D3—41no—
528C2×D3—41no—
529C2×D3—41no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—32no—
535C3×C4—42no—
536C3×C4—41no—
537C3×C4—41no—
538C3×C4—61no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—122no—
542C3×C4—121no—
543C3×C4#67⋊C411yescharacteristic
544C3×C4#88411yescharacteristic
545C3×C4C4×#6711yescharacteristic
546C3×C4D4×Dic311yescharacteristic
547C3×C4D4×Dic311yescharacteristic
548C3×C4#93811yescharacteristic
549C3×C4#93811yescharacteristic
550C3×C4#93911yescharacteristic
551Dic3—21no—
552Dic3—21no—
553Dic3—21no—
554Dic3—42no—
555Dic3—41no—
556Dic3—122no—
557Dic3—122no—
558Dic3—124no—
559Dic3#83712yescomplemented
560C32#198011yescharacteristic, complemented, Sylow
561C23—21no—
562C23—61no—
563C23D3×#6711yescharacteristic
564Q8—21no—
565Q8—21no—
566Q8—61no—
567Q8—61no—
568D4—21no—
569D4—21no—
570D4—41no—
571D4—41no—
572D4—61no—
573D4—61no—
574D4—122no—
575D4—122no—
576D4—121no—
577D4—121no—
578C2×C4—21no—
579C2×C4—31no—
580C2×C4—31no—
581C2×C4—31no—
582C2×C4—31no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—61no—
588C2×C4—121no—
589C2×C4—121no—
590C2×C4—121no—
591C2×C4—121no—
592C2×C4—121no—
593C2×C4—182no—
594C2×C4—361no—
595C2×C4—361no—
596C2×C4C2×D3×Dic311yescharacteristic
597C2×C4#380411yescharacteristic
598C2×C4#380511yescharacteristic
599C2×C4D3×#6711yescharacteristic
600C2×C4D3×#6711yescharacteristic
601C2×C4#381111yescharacteristic
602C8—62no—
603C8—182no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—82no—
614C2×C3—81no—
615C2×C3—81no—
616C2×C3—241no—
617C2×C3D3×#10411yescharacteristic
618C2×C3#482111yescharacteristic
619C2×C3#495711yescharacteristic
620C2×C3#522111yescharacteristic
621C2×C3C2×#83711yescharacteristic
622C2×C3#523611yescharacteristic
623D3—81no—
624C22—21no—
625C22—21no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—121no—
630C22—121no—
631C22—121no—
632C22#6395911yescharacteristic
633C22D3×#21711yescharacteristic
634C22#6397911yescharacteristic
635C4—32no—
636C4—41no—
637C4—61no—
638C4—61no—
639C4—61no—
640C4—122no—
641C4—121no—
642C4—362no—
643C4#6395811yescharacteristic
644C4#6397011yescharacteristic
645C4Dic3×#6711yescharacteristic
646C4#67⋊Dic311yescharacteristic
647C3—21no—
648C3#7035811yescharacteristic, complemented
649C3#7181811yescharacteristic, complemented
650C2—21no—
651C2—21no—
652C2—81no—
653C2—241no—
654C2D3×#83711yescharacteristic
655C2#1059167011yescharacteristic
656C2#1059170711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5832C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#63664C2semidirect
3. C2×C3×#837C2semidirect
4. C4×Dic3⋊Dic3C2semidirect
5. C2×#63569C2semidirect
6. C2×#63568C2semidirect
7. Dic3×#208C2semidirect
14. C3×#947C4semidirect
15. C3×#944C4semidirect
16. C3×#940C4semidirect
19. C3×#936C4semidirect
41. C2×#837D3semidirect
74. #3748D4semidirect
89. C3×#208D4semidirect
109. #947Dic3semidirect
110. #944Dic3semidirect
111. #940Dic3semidirect
114. #936Dic3semidirect
291. #208#67semidirect
318. C3×Dic3#104semidirect
559. Dic3#837semidirect
560. C32#1980semidirect
648. C3#70358semidirect
649. C3#71818semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#58322
C2×#636642
C2×C3×#8372
C4×Dic3⋊Dic32
C2×#635692
C2×#635682
Dic3×#2082
#718183
#703583